DOCSLIB.ORG

Ratios: (Gyrofrequency/Collision Freq), (Gyroradius/ Device L)

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Ratios: (Gyrofrequency/Collision Freq), (Gyroradius/ Device L) Ratios: (gyrofrequency/collision freq), (gyroradius/ device L) electrons (Te ~ 2 eV, Ar) 15 16 -3 Since nn typically 10 – 10 cm currently, need B > ~ 200 G, so electrons may already be magnetized in some expts. ions (Ti ~ .05 eV, Ar) Since mi >> me, Ti << Te (while σin ~ 10 σen), need larger B to magnetize the ions: B > 0.5 – 2 T with current nn (argon) dust (ρd ~ 2g/cc, Ar, Tn ~ 300 K) Larger B needed as R↑, nn ↑, Td ↑, φ↓, L ↓ e.g., φ ~ - 4 V, R ~ 0.1 µm, P ~ 10 Pa, B >> 30 T as above, with P ~ 0.13 Pa, B >> 0.4 T Use of small dust having surface plasmon resonance? • Background: Surface Plasmon (ne wave) at interface Polarizability of small sphere 2R << λ light ε ε0 E-field e-cloud resonance Re ε = - 2 ε0 (Im ε << 1) surface plasmon - optical, near-UV (Au, Ag) Possible way to see nano-sized dust in plasma • Absorption and scattering enhanced at SP frequency • Use of dust with SP - ‘see’ nanoparticle transport in plasma - ‘see’ waves, etc. in plasma with magnetized dust (R~ 20 nm, B ~ 2T) Possible diagnostic for dust waves in magnetized dusty plasma • Nm sized dust could be magnetized Ag ~ 40 nm e.g. Ar, Te ~ 2 eV, B ~ 2 T, P < 3 Pa ρd < ~ 1 cm, ωcd > νd , F Lorentz > F gravity • ‘See’ waves by enhanced absorption by dust with SP Compression - dark; rarefaction - light n ~ 109 cm-3 d Absorption coeff. ~ 0.1 /cm λ ~ 350 nm (Re ε ~ -2) Rosenberg & Shukla, APL 86, 2005 Theory has been done for dust wave instabilities under the following conditions, but not aware of experiments to test these : Unmagnetized dust, magnetized ions e.g. Hall current (E x B) driven instabilities drift instabilities Magnetized dust e.g. electrostatic dust cyclotron instability (higher harmonics too) waves in plasma crystals Possible constraint related to Electrostatic Dust Cyclotron waves EDC wave: in long λ limit, k┴ρd << 1, 2 2 2 ω ~ ωcd (1+Δ), Δ ~ k┴ csd /2ωcd << 1, where the dust acoustic speed csd ~ λDiωpd (for Te >> Ti) -4 9 e.g. Ti ~ 0.2 eV, nd/ni ~ 10 , md/mp ~ 2 x 10 (R ~ 0.1 µm), B ~ 2 T λ┴ > 7 cm ( λ║ > λ┴) , larger device ? Estimates of B for controlling motion of paramagnetic dust Induced magnetic moment Ratio of forces: attractive magnetic dipole-dipole to repulsive Coulomb B d Tune grain interactions via FM, using superparamagnetic grains e.g., φ ~ - 4 V, R ~ 5 µm, d ~ 100 µm, µ ~ 3 , B ~ 200 G , FM/Fe ~ 0.1 as above with R ~ 0.3 µm, FM/Fe ~ 0.1 requires B ~ 5 T as R ↓ , B ↑ Magnetic packing force: magnetic grains move to regions of max. B Ratio of forces: magnetic packing to attractive magnetic dipole-dipole e.g., as in previous example, R ~ 5 µm, d ~ 100 µm, µ ~ 3, B ~ 200 G, FMP/FM > 1 if ∂B/∂z ~ 6 G/cm 3 Levitate [1] : FMP, grav. force both proportional to R e.g., µ~ 3, B ~ 1000 G, ∂B/∂z ~ 20 G/cm, ρd ~ 2g/cc [1] Samsonov et al, NJP, 2003 Some physics issues that could be studied at large B ~ T Charging: Debye sphere, anisotropic, E x B of electrons (ρe ~ R) ? Forces: effect of magnetized ions (ρi ~200 µm) on ion drag? Fusion: how does B affect structure of ablation cloud around large grain? Waves: observe EDC waves and instabilities? Crystal: how do magnetized ions & electrons affect structure and waves? (e.g., ρi ~ lattice spacing, E x B motion in sheath ) Crystal: can crystal form if dust is magnetized (smaller R, lower Zd) ? Some physics issues that could be studied at B < T (magnetized ions and/or electrons, unmagnetized dust) Waves: observe dust wave instabilities driven by electron or ion cross –field drifts, including Hall current instabilities, and drift wave instabilties? Paramag. dust: tune behavior of dust acoustic waves (attractive force along B, repulsive perpendicular to B)? Paramag. dust: tune spacings and structure in a plasma crystal by changing magnitude and orientation of B? Paramag. dust: use FM + Fe force to levitate one type of grain, Fe to levitate other type, form binary crystal? .
Load more

Recommended publications
  • Ion Cyclotron and Heavy Ion Effects on Reconnection in a Global Magnetotail R
    JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, A09206, doi:10.1029/2004JA010385, 2004 Ion cyclotron and heavy ion effects on reconnection in a global magnetotail R. M. Winglee Department of Earth and Space Sciences, University of Washington, Seattle, Washington, USA Received 12 January 2004; revised 21 May 2004; accepted 8 July 2004; published 22 September 2004. [1] Finite ion cyclotron effects play a significant role in determining the dynamics of the neutral sheet. The demagnetization of the ions facilitates reconnection and produces an electric field perpendicular to the direction of the tail currents. This in-plane electric field drives field-aligned currents and an out-of-plane (or core) magnetic field in conjunction with the generation of flux ropes. In addition to these electromagnetic effects, it is shown that ion cyclotron effects lead to the preferential convection of plasma from the dawnside to the duskside. This convection is consistent with results from single- particle tracking but differs from ideal MHD treatment where the flow occurs symmetrically around the Earth. A physical manifestation of these asymmetric particle trajectories is the wrapping of the field-aligned current between the region 1 currents and the region 2 and/or region 0 currents. In addition, localized density enhancements and depletions are seen in the tail where the local heavy ion density can be substantially elevated over ionospheric conditions. Because of the local density variations, reconnection across the tail is inhomogeneous. Reconnection is initiated postmidnight and then sweeps across to the dawn and dusk flanks within a few minutes. Because of this spatial variation, the ejection plasmoid is actually U-shaped and the subsequent flux rope formation is highly skewed.
    [Show full text]
  • Searches for Point-Like Sources of Astrophysical Neutrinos with the Icecube Neutrino Observatory
    Searches for Point-like Sources of Astrophysical Neutrinos with the IceCube Neutrino Observatory By Jacob Feintzeig Adissertationsubmittedinpartialfulfillmentof the requirements for the degree of Doctor of Philosophy (Physics) at the UNIVERSITY OF WISCONSIN–MADISON 2014 Date of final oral examination: August 22, 2014 The dissertation is approved by the following members of the Final Oral Committee: Amy Connolly, Assistant Professor, Physics John S Gallagher, Professor, Astronomy Francis Halzen, Professor, Physics Albrecht Karle, Professor, Physics Dan McCammon, Professor, Physics i ACKNOWLEDGMENTS Iamincrediblyfortunatetohavemanysupportivementorsandpeerswhomadethis work possible. I’d like to first thank my advisor Albrecht for giving me the opportunity to work on IceCube, for providing valuable guidance and advice throughout this project, and for giving me the independence to pursue ideas I found interesting. I’d like to thank Naoko for helping me troubleshoot analysis problems and brainstorm ideas when I was stuck, and providing advice from all issues large to small. Thanks to Chad for encouraging me to think in new ways and approach problems from di↵erent angles. I’d like to express my appreciation for Chris Wendt and Gary Hill for teaching me how to do statistics, dig into the details of the data, and complete a rigorous analysis. Thanks to John Kelley for helping me get to Pole and for teaching me how to do everything once we were there. Thanks to Dima and Juan Carlos for explaining the technical details of reconstruction and simulation in many times of need. Many thanks to Markus for our many valuable physics discussions. Ioweadebtofgratitudetothelargenumberofstudentsandpostdocswhohelpedme debug my code, brainstorm ideas, develop analyses, and o↵ered their support in a myriad of small, invisible ways (not to mention provided entertaining office banter).
    [Show full text]
  • Icecube Searches for Neutrinos from Dark Matter Annihilations in the Sun and Cosmic Accelerators
    UNIVERSITE´ DE GENEVE` FACULTE´ DES SCIENCES Section de physique Professeur Teresa Montaruli D´epartement de physique nucl´eaireet corpusculaire IceCube searches for neutrinos from dark matter annihilations in the Sun and cosmic accelerators. THESE` pr´esent´ee`ala Facult´edes sciences de l'Universit´ede Gen`eve pour obtenir le grade de Docteur `essciences, mention physique par M. Rameez de Kozhikode, Kerala (India) Th`eseN◦ 4923 GENEVE` 2016 i Declaration of Authorship I, Mohamed Rameez, declare that this thesis titled, 'IceCube searches for neutrinos from dark matter annihilations in the Sun and cosmic accelerators.' and the work presented in it are my own. I confirm that: This work was done wholly or mainly while in candidature for a research degree at this University. Where any part of this thesis has previously been submitted for a degree or any other qualifica- tion at this University or any other institution, this has been clearly stated. Where I have consulted the published work of others, this is always clearly attributed. Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work. I have acknowledged all main sources of help. Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself. Signed: Date: 27 April 2016 ii UNIVERSITE´ DE GENEVE` Abstract Section de Physique D´epartement de physique nucl´eaireet corpusculaire Doctor of Philosophy IceCube searches for neutrinos from dark matter annihilations in the Sun and cosmic accelerators.
    [Show full text]
  • GZK Neutrino Search with the Icecube Neutrino Observatory Using New Cosmic Ray Background Rejection Methods
    GZK Neutrino Search with the IceCube Neutrino Observatory using New Cosmic Ray Background Rejection Methods THÈSE NO 5813 (2013) PRÉSENTÉE LE 28 JUIN 2013 À LA FACULTÉ DES SCIENCES DE BASE LABORATOIRE DE PHYSIQUE DES HAUTES ÉNERGIES 1 PROGRAMME DOCTORAL EN PHYSIQUE ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES PAR Shirit COHEN acceptée sur proposition du jury: Prof. O. Schneider, président du jury Prof. M. Ribordy, directeur de thèse Dr P. North, rapporteur Prof. E. Resconi, rapporteur Prof. D. Ryckbosch, rapporteur Suisse 2013 Acknowledgements It has been a great privilege and pleasure to take part in the IceCube collaboration research work during these past years. The effort to solve challenging physics questions within an international working group together with collaboration meetings and work stay abroad had been the most rewarding during this thesis work. I thank my advisor Mathieu Ribordy for giving me the opportunity to join IceCube, for his strong physics understanding and sharp ideas during the research work, and for his support in finalising the analysis. The work would not have been possible without the day-to-day guidance of Levent Demiroers, and almost as important, his good company in the office. I am also grateful to Ronald Bruijn for his help and patience in the past year and friendly discussions aside from work. Arriving at the finishing line of this doctoral studies within our tiny IceCube group in EPFL is an achievement you have all helped to realise and I am grateful for it. This research work was developed within the EHE/Diffuse working group in IceCube with its collaborators in the US, Europe and Japan — and accordingly complicated phone meetings schedule.
    [Show full text]
  • Problems for the Course F5170 – Introduction to Plasma Physics
    Problems for the Course F5170 { Introduction to Plasma Physics Jiˇr´ı Sperka,ˇ Jan Vor´aˇc,Lenka Zaj´ıˇckov´a Department of Physical Electronics Faculty of Science Masaryk University 2014 Contents 1 Introduction5 1.1 Theory...............................5 1.2 Problems.............................6 1.2.1 Derivation of the plasma frequency...........6 1.2.2 Plasma frequency and Debye length..........7 1.2.3 Debye-H¨uckel potential.................8 2 Motion of particles in electromagnetic fields9 2.1 Theory...............................9 2.2 Problems............................. 10 2.2.1 Magnetic mirror..................... 10 2.2.2 Magnetic mirror of a different construction...... 10 2.2.3 Electron in vacuum { three parts............ 11 2.2.4 E × B drift........................ 11 2.2.5 Relativistic cyclotron frequency............. 12 2.2.6 Relativistic particle in an uniform magnetic field... 12 2.2.7 Law of conservation of electric charge......... 12 2.2.8 Magnetostatic field.................... 12 2.2.9 Cyclotron frequency of electron............. 12 2.2.10 Cyclotron frequency of ionized hydrogen atom.... 13 2.2.11 Magnetic moment.................... 13 2.2.12 Magnetic moment 2................... 13 2.2.13 Lorentz force....................... 13 3 Elements of plasma kinetic theory 14 3.1 Theory............................... 14 3.2 Problems............................. 15 3.2.1 Uniform distribution function.............. 15 3.2.2 Linear distribution function............... 15 3.2.3 Quadratic distribution function............. 15 3.2.4 Sinusoidal distribution function............. 15 3.2.5 Boltzmann kinetic equation............... 15 1 CONTENTS 2 4 Average values and macroscopic variables 16 4.1 Theory............................... 16 4.2 Problems............................. 17 4.2.1 RMS speed........................ 17 4.2.2 Mean speed of sinusoidal distribution........
    [Show full text]
  • First in Situ Evidence of Electron Pitch Angle Scattering Due to Magnetic
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by UCL Discovery PUBLICATIONS Journal of Geophysical Research: Space Physics RESEARCH ARTICLE First in situ evidence of electron pitch angle scattering due 10.1002/2016JA022409 to magnetic field line curvature in the Ion diffusion region Key Points: Y. C. Zhang1,2,3,4, C. Shen5, A. Marchaudon3,4, Z. J. Rong2, B. Lavraud3,4, A. Fazakerley6, Z. Yao6, • First multispacecraft analysis of 6 7 5 1 magnetic field curvature in the ion B. Mihaljcic ,Y.Ji ,Y.H.Ma , and Z. X. Liu diffusion region 1 2 • Electron dynamics is analyzed as a State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing, China, Key function of magnetic field curvature Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, • Observational evidence for magnetic China, 3Institut de Recherche and Astrophysique et Planétologie, Université de Toulouse (UPS), Toulouse, France, 4Centre curvature-induced electron pitch National de la Recherche Scientifique, UMR 5277, Toulouse, France, 5Shenzhen Graduate School, Harbin Institute of angle scattering Technology, Shenzhen, China, 6Mullard Space Science Laboratory, University College London, London, UK, 7State Key Laboratory for Turbulence & Complex Systems, Peking University, Beijing, China Correspondence to: Y. C. Zhang, Abstract Theory predicts that the first adiabatic invariant of a charged particle may be violated in a region [email protected] of highly curved field lines, leading to significant pitch angle scattering for particles whose gyroradius are comparable to the radius of the magnetic field line curvature.
    [Show full text]
  • High-Resolution, High-Accuracy Plasma, Electric, and Magnetic Field Measurements for Discovery of Kinetic Plasma Structures and Processes in the Evolving Solar Wind
    High-resolution, high-accuracy plasma, electric, and magnetic field measurements for discovery of kinetic plasma structures and processes in the evolving solar wind J. J. Podesta, J. E. Borovsky, J. T. Steinberg, R. Skoug, J. Birn, S. P. Gary, S. R. Cranmer, G. Zank, G. Li, J. T Gosling, N. A. Schwadron, J. Giacalone, K. W. Ogilvie, D. A. Roberts, A. Szabo, J. A. Slavin, T. Chang, J. D. Richardson, R. P. Lin, J. Luhmann, P. J. Kellogg, C. T. Russell, L. Jian, C. W. Smith, A. Bhattacharjee, B. D. G. Chandran, O. Alexandrova, V. Pierrard, F. Sahraoui, M. L. Goldstein, M. Velli, S. D. Bale To discover and understand the mechanisms responsible for the heating and acceleration of the solar wind is an important goal of solar and space physics that has stimulated scientific study for many years. Although significant progress has occurred in the last few decades, to achieve this goal requires the ground truth provided by an advanced generation of in situ spacecraft measurements. To solve the mystery of solar wind heating and acceleration requires direct observational knowledge of the solar wind structures, plasma waves, and wave-particle interactions that play a dominant role in these processes. Since the relevant mechanisms operate at kinetic scales, it is clear that high accuracy, high cadence plasma and wave measurements are essential to pave the way for the science that will eventually solve this mystery. Progress toward a solution of this fundamental issue requires that these next generation measurements be performed in the inner heliosphere and at 1 AU in the coming decades.
    [Show full text]
  • Synchrotron Radiation
    Synchrotron Radiation The synchrotron radiation, the emission of very relativistic and ultrarelativistic electrons gyrating in a magnetic field, is the process which dominates much of high energy astrophysics. It was originally observed in early betatron experiments in which electrons were first accelerated to ultrarelativistic energies. This process is responsible for the radio emission from the Galaxy, from supernova remnants and extragalactic radio sources. It is also responsible for the non-thermal optical and X-ray emission observed in the Crab Nebula and possibly for the optical and X-ray continuum emission of quasars. The word non-thermal is used frequently in high energy astrophysics to describe the emission of high energy particles. This an unfortunate terminology since all emission mechanisms are ‘thermal’ in some sense. The word is conventionally taken to mean ‘continuum radiation from particles, the energy spectrum of which is not Maxwellian’. In practice, continuum emission is often referred to as ‘non-thermal’ if it cannot be described by the spectrum of thermal bremsstrahlung or black-body radiation. 1 Motion of an Electron in a Uniform, Static Magnetic field We begin by writing down the equation of motion for a particle of rest mass m0, charge ze and Lorentz factor γ = (1 − v2/c2)−1/2 in a uniform static magnetic field B. d (γm0v) = ze(v × B) (1) dt We recall that the left-hand side of this equation can be expanded as follows: d dv 3 (v · a) m0 (γv) = m0γ + m0γ v (2) dt dt c2 because the Lorentz factor γ should be written γ = (1 − v · v/c2)−1/2.
    [Show full text]
  • NRL: Plasma Formulary 5B
    Naval Research Laboratory Washington, DC 20375-5320 NRL/PU/6790--04-477 NRL Plasma Formulary Revised 2004 Approved for public release; distribution is unlimited. Form Approved Report Documentation Page OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 2. REPORT TYPE 3. DATES COVERED 2004 N/A - 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER NRL: Plasma Formulary 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER Naval Research Laboratory Washington, DC 20375-5320 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release, distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17.
    [Show full text]
  • Cyclotron & Synchrotron Radiation
    Cyclotron & Synchrotron Radiation Synchrotron Radiation is radiation emerging from a charge moving relativistically that is accelerated by a magnetic field. The relativistic motion induces a change in the radiation pattern which is very collimated (beaming, see Lecture 4). Cyclotron Radiation: power & radiation pattern To understand synchrotron radiation let’s first begin with the non-relativistic motion of a charge accelerated by a magnetic field. That the acceleration is given by an electric field, gravity or a magnetic field does not matter for the charge, which will radiate according to the Larmor’s formula (see Lecture 5) Direction of acceleration Remember that the radiation pattern is a Radiation pattern torus with a sin^2 dependence on the angle of emission: Cyclotron Radiation: gyroradius So let’s take a charge, say an electron, and let’s put it in a uniform B field. What will happen? The acceleration is given by the Lorentz force. If the B field is orthogonal to v then: F=qvB Equating this to the centripetal force gives the “larmor radius”: m v2 mv F= =qvB→r L= r L qB We can also find the cyclotron angular frequency: 2 m v 2 qB F= =m ω R→ω = R L L m Cyclotron Radiation: cyclotron frequency From the angular frequency we can find the period of rotation of the charge: 2 π 2 π m T= = ωL qB Note that the period of the particle does not depend on the size of the orbit and is constant if B is constant. The charge that is rotating will emit radiation at a single specific frequency: ω qB ν = L = L 2π 2π m Direction of acceleration Radiation pattern Cyclotron Radiation: power spectrum ωL qB Since the emission appears at a single frequency ν = = L 2π 2π m and the dipolar emission pattern is moving along the circle with constant velocity, the electric field measured will vary sinusoidally and the power spectrum will show a single frequency (the Larmor or cyclotron frequency).
    [Show full text]
  • Electron-Scale Physics in Space Plasma
    Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1453 Electron-scale physics in space plasma Thin boundaries and magnetic reconnection CECILIA NORGREN ACTA UNIVERSITATIS UPSALIENSIS ISSN 1651-6214 ISBN 978-91-554-9755-2 UPPSALA urn:nbn:se:uu:diva-307955 2016 Dissertation presented at Uppsala University to be publicly examined in Polhemsalen, Ångström Laboratory, Lägerhyddsvägen 1, Uppsala, Friday, 20 January 2017 at 10:00 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Dr/Lecturer Jonathan Eastwood. Abstract Norgren, C. 2016. Electron-scale physics in space plasma. Thin boundaries and magnetic reconnection. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1453. 68 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9755-2. Most of the observable Universe consists of plasma, a kind of ionized gas that interacts with electric and magnetic fields. Large volumes of space are filled with relatively uniform plasmas that convect with the magnetic field. This is the case for the solar wind, and large parts of planetary magnetospheres, the volumes around the magnetized planets that are dominated by the planet's internal magnetic field. Large plasma volumes in space are often separated by thin extended boundaries. Many small-scale processes in these boundaries mediate large volumes of plasma and energy between the adjacent regions, and can lead to global changes in the magnetic field topology. To understand how large-scale plasma regions are created, maintained, and how they can mix, it is important understand how the processes in the thin boundaries separating them work.
    [Show full text]
  • Guiding Center Motion
    GUIDING CENTER MOTION H.J. de Blank FOM Institute DIFFER – Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM, P.O. Box 1207, 3430 BE Nieuwegein, The Netherlands, www.differ.nl. ABSTRACT Secondly, the Coulomb force is a long range interaction. In a well-ionized plasma, particles rarely suffer large-angle The motion of charged particles in slowly varying electro- deflections in two-particle collisions. Rather, their orbits are magnetic fields is analyzed. The strength of the magnetic deflected through weak interactions with many particles si- field is such that the gyro-period and the gyro-radius of the multaneously. Hence, the effects of collisions can be best particle motion around field lines are the shortest time and described statistically, in terms of distributions of particles. length scales of the system. The particle motion is described The kinetic equation for the particle distribution function as the sum of a fast gyro-motion and a slow drift velocity. will be discussed at the end of this chapter, with emphasis on the role of the particle orbits, not the collisions. The equations of motion of a particle with mass m and I. INTRODUCTION charge q in electromagnetic fields E(x, t) and B(x, t) are, The interparticle forces in ordinary gases are short-ranged, q x˙ = v, v˙ = (E + v B), (1) so that the constituent particles follow straight lines between m × collisions. At low densities where collisions become rare, N the gas molecules bounce up and down between the walls of where the dot denotes the time derivative. Each of the the containing vessel before experiencing a collision.
    [Show full text]